If you want to keep several days worth of backups, your storage requirements will grow dramatically with this approach. A tool called rdiff-backup, based on rsync, gets around this issue.

Agreed, I use rdiff-backup because I found my rsync backups were getting cluttered with old files, and sometimes the lack of versioned backups was problematic. I'm a big fan of rdiff-backup. I don't think it actually leverages rsync, as such, but librsync. It's a great tool.

I think that rsync is great but tools like dar, attic, bup, rdiff-backup or obnam are better. I use obnam, as it does "snapshot backups" with deduplication.